What is 24.2757575... as a Fraction?

24.275 equals 8011330 as a fraction.

How do you turn 24.275 repeating into a fraction?

Detailed Answer:

Step 1: To convert 24.275 repeating into a fraction, begin writing this simple equation:

n = 24.275 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (75) and 1 digit in the non-repeating part (2). Multiply both sides by 10³ = 1000.

1000 × n = 24275.75 (equation 2)

Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.

1000 × n = 24275.75
  10 × n = 24.275
 990 × n = 24033

24033990 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 3 (the GCF - greatest common factor).

n = 24033990 = 24033 ÷ 3990 ÷ 3 = 8011330. So,

24.275 = 8011330 as the lowest possible fraction.

As the numerator is greater than the denominator, we have an improper fraction, so we can also express it as a mixed number, thus 8011330 is also equal to 2491330 when expressed as a mixed number.

The repeating decimal 24.275 (vinculum notation) has a repeated block length of 2. It is also represented as 24.2757575... (ellipsis notation) which equals approximately 24.27575757575 (decimal approximation)(*).

The recurring decimal 24.275 can be written as a ratio of two integers having 8011 as the numerator and 330 as the denominator. So, it is a rational number (named after ratio). It can be shown that a number is rational if its decimal representation is repeating or terminating.

(*) At present, there is no single universally accepted notation or phrasing for repeating decimals.